Mathematics
In a quadrilateral ABCD, ∠B = 90°. If AD2 = AB2 + BC2 + CD2, Prove that ∠ACD = 90°.
Pythagoras Theorem
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Answer
In right angle triangle ABC,
By pythagoras theorem,
AC2 = AB2 + BC2 …….(i)
Given,
AD2 = AB2 + BC2 + CD2
Putting value of AB2 + BC2 from eqn (i) we get,
AD2 = AC2 + CD2
∴ △ACD is a right angled triangle.
In △ACD,
∠ACD = 90° i.e. angle opposite to hypotenuse = 90° (By converse of pythagoras theorem.)
Hence, proved that ∠ACD = 90°.
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